Method and Apparatus for Over-the-Air Neural Networks via Reconfigurable Intelligent Surfaces

1. A method for implementing an over-the-air neural network (OANN) comprising: receiving, at a relay receiver of a relay node, a signal of interest from a transmitter; directionally re-transmitting the signal of interest from each of a plurality of relay transmitters of the relay node to a corresponding one of a plurality of programmable reconfigurable intelligent surfaces (RIS); reflecting, by each of the plurality of RIS, the corresponding re-transmitted signal of interest; adjusting, by a neural network controller, a reflection angle of each of the plurality of RIS to direct the reflected signals of interest to combine in a deterministic manner at the relay receiver, wherein the adjusting operates the plurality of RIS to create the signal reflections to emulate determined finite impulse response (FIR) filters; and training the OANN using weights of neurons drawn from a finite set of distinct channel impulse responses (CIR) that correspond to finite impulse response (FIR) filters realizable by the plurality of RIS, wherein each CIR is determined by activating a different configuration of the plurality of programmable RIS and the deterministic combination of reflected signals at the relay receiver is determinative of the output of a convolution step.

2. The method of claim 1, wherein the relay receiver is an omnidirectional antenna.

3. The method of claim 1, wherein the plurality of transmitters are directional transmitters.

4. The method of claim 1, wherein a maximum number of CIR and corresponding FIR filters implementable by the OANN is at least partially determined by a maximum number of deterministic sets of reflections producible by the plurality of RIS.

5. The method of claim 4, wherein the maximum number of deterministic sets of reflections producible by the plurality of RIS is scalable according to a number of possible phase changes of each RIS, a number of the plurality of RIS, and a number of directional antennas at the relay node.

6. The method of claim 1, the step of adjusting further comprising reconfiguring, by the neural network controller, reflection angles of the plurality of RIS to form an updated RIS configuration corresponding to a next convolutional.

7. The method of claim 1, wherein the neural network controller is in communication with the plurality of RIS via a dedicated control plane configured to connect the relay node to the plurality of RIS.

8. The method of claim 1, further comprising, by the neural network controller, at least one additional digital-only processing operation including at least one of a rectified linear unit (ReLu) activation, a batch normalization, a max pooling, a fully connected layer, or combinations thereof.

9. An over-the-air neural network system comprising: a transmitter system operable to transmit signals of interest; a relay node comprising: a relay receiver, a plurality of relay transmitters; a neural network controller; and a plurality of programmable reconfigurable intelligent surfaces (RIS), each of the plurality of RIS corresponding to one of the plurality of relay transmitters, each RIS operable to directionally reflect signals with desired channel transformations; wherein the relay receiver is operable to receive the signals of interest and forward the signals of interest to the relay transmitters, each of the relay transmitters operative to directionally re-transmit the signals of interest to a corresponding one of the plurality of programmable RIS, and each RIS is operable to reflect the corresponding re-transmitted signals of interest, and the neural network controller is operable to adjust a reflection angle of each of the plurality of RIS to direct the reflected signals of interest with desired channel transformations to combine in a deterministic manner at the relay receiver, wherein adjustment of the reflection angle operates the plurality of RIS to create the signal reflections to emulate determined finite impulse response (FIR) filters; and wherein the over-the-air neural network system comprises a convolutional neural network trained using weights of neurons drawn from a finite set of distinct channel impulse responses (CIR) that correspond to finite impulse response (FIR) filters realizable by the plurality of RIS, wherein each CIR is determined by activating a different configuration of programmable RIS, and reflected signals combine at the relay receiver to determine the output of the convolution step.

10. The system of claim 9, wherein the relay receiver is an omnidirectional antenna.

11. The system of claim 9, wherein the relay transmitters are directional antennas.

12. The system of claim 9, wherein each RIS is a planar array of passive reflective antenna.

13. The system of claim 12, wherein each passive reflective antenna each includes a selectable range of programmable impedance matching circuits.

14. The system of claim 13, wherein: selective activation of one or more of the programmable impedance matching circuits changes an impedance of a corresponding one of the reflective antenna; changing the impedance of the corresponding one of the reflective antennas alters an antenna reflection coefficient of the corresponding reflective antenna, thereby changing a phase of the reflected signal.